There are several sections of the Unity End-User License Agreement (which is for version 4.x as I write this, although earlier versions are similar) that pertaining to this issue.
The most directly relevant is section 3, which reads (in part):
You will not delete or in any manner alter any Unity or third-party
copyright, trademark or other proprietary rights notices or markings
appearing on or in the Software (including the runtime portion
This is a pretty straightforward answer to your question: no, you are not permitted to remove the Unity splash screen from your Unity-based game.
There are other restrictions, such as section 2.f, which reads (in part):
General Restrictions. Except as expressly specified in this Agreement,
you may not: (i) copy (except in the course of loading or installing)
or modify or create derivative works of the Software;
Accordingly, you agree not to disassemble, decompile or reverse
engineer the Software, in whole or in part, or permit or authorize a
third party to do so, except to the extent such activities are
expressly permitted by law notwithstanding this prohibition.
For the terms of the license, the term "Software" refers to "all 4.x versions and updates of all the Unity software products identified on Unity’s website." Further, the agreement is governed by the laws of Denmark, a fact which probably does not particularly apply to this question but is nonetheless worth noting.
Your technique for digging around in the final binaries of the game and gutting the default splash screen pretty clearly violates the above; your only recourse for splash screen modification is going to be whatever is built-in to the version of Unity you have. Your technique violates the license agreement.